The evaluation of rate constants in rate laws containing two terms

A simple computerized method using APL is described which gives the rate constants for systems obeying the rate law –d[A]/dt = k₁[A][B] + k₂[A] ^m [B]^l from sets of concentrations and times. Applications are discussed.     

Characterization of Sol-gel bioencapsulates for ester hydrolysis and synthesis

Candida rugosa lipase was entrapped in silica sol-gel particles prepared by hydrolysis of methyltrimethoxysilane and assayed by p-nitrophenyl palmitate hydrolysis, as a function of pH and temperature, giving pH optima of 7.8 (free enzyme) and 5.0–8.0 (immobilized enzyme). The optimum temperature for the immobilized enzyme (50–55°C) was 19°C higher than for the free enzyme. Thermal, operational, and storage stability were determined with n-butanol and bytyric acid, giving at 45°C a half-life 2.7 times greater for the immobilized enzyme; storage time was 21 d at room temperature. For ester synthesis, the optimum temperature was 47°C, and high esterification conversions were obtained under repeated batch cycles (half-life of 138 h).     

Pulse photolysis rate constants of the decay of ester peroxide radicals

Pulse photolysis measurements of rate constants of the decay of peroxide radicals for seven saturated acetates have revealed their increase with shortening alkyl chain. It is attributed to the high rate constants of the interaction of -acyloxyperoxide radicals ((3±1)×10⁸l/mol s) compared to those for remote peroxide ones.

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. , - (3±1)×10⁸ /. ) .

     

Test of the procedure for obtaining detailed endothermic rate constants from microscopic reversibility

Experimental data concerning the effect of varying reagent vibrational, rotational and translational energy on the rates of endothermic reactions can be obtained from the application of microscopic reversibility to the corresponding exothermic processes. A 3D classical trajectory computation has been performed to test this procedure. On the basis of this study we conclude that the ‘triangle plots’ of endothermic detailed rate constants published previously can be depended on to 5–10% theoretical accuracy (expressed as a percentage of the maximum endothermic rate constant).     

Stability and hydrolysis rate constants of aqueous solutions of mercuric acetate and methylmercuric acetate

Rate constants for the hydrolysis of mercuric acetate in the range 1.2 × 10⁻³ – 1.25 × 10⁻² M have been determined at 25° and one atmosphere pressure. The hydrolysis rate has also been studied at pressures up to 1500 bar for concentrations of mercuric acetate less than 2 × 10⁻³ M. Mercuric acetate is slowly hydrolysed in water and the rate of hydrolysis increases with increasing pressure; the volume of activation is −(7.0 ± 0.6) cm³ mole⁻¹. The hydrolysis of mercuric acetate becomes more complex with increasing concentration. At low concentrations the kinetic data were fitted with a single first-order rate constant while at concentrations greater than 7 × 10⁻³ M the data were fitted by two first-order rate constants. By contrast, aqueous solutions of methylmercuric acetate were found to be quite stable, even under pressures of 1500 bar. The molal conductance of methylmercuric acetate was investigated and the dissociation constant determined to be (2.8 ± 0.2) × 10⁻⁴ M.     

Determination of microscopic rate constants for CO binding and migration in myoglobin encapsulated in silica gels

CO rebinding kinetics after nanosecond photolysis of myoglobin encapsulated in wet silica gels exhibits an enhanced geminate phase that allows the determination of the microscopic rate constants and the activation barriers for distinct ligand docking sites inside the protein matrix. Using a maximum entropy method, we demonstrate that the geminate phase can be well-described by a biphasic lifetime distribution, reflecting rebinding from the distal and proximal sites. Microscopic rates and activation barriers were estimated using a four-state model.     

Contrasting effects of redox potentials on the rate constants of oxidation and hydrolysis reactions in ruthenium complexes

We report in this work the rate constant of oxidation by peroxydisulfate of the ammine ruthenium center in [(bpy)₂Ru(μ-5-CNphen)Ru(NH₃)₅]⁴⁺ (bpy?=?2,2′-bipyridine and 5-CNphen?=?5-cyano-1,10-phenanthroline) and the rate constant of hydrolysis of coordinated acetonitrile in [Ru(TPTZ)(bpy)(CH₃CN)]²⁺ (TPTZ = 2,4,6-tris(2-pyridil)-1,3,5-triazine). With these data and literature values of related reactions, we establish the existence of contrasting effects of redox potentials of Ru^3+/2+ couples on the rates of both processes.     

Amide group catalysis of ester hydrolysis

Hydrolysis of phenyl-N-acetylanthranilate 1 (Ar = Ph) to N-acetyl anthranilie acid 3 is base catalysed and occurs through the intermediacy of 2-methyl-3,1-benzoxazin-4-one 4. Above pH 6 the formation of 4 from 1 is faster than the base (or acid) catalysed ring opening of 4 to 3. Electron-withdrawing substituents in the ester moiety (e.g. 1, Ar = p-NO₂C₆H₄) aid cyclization to 4 relative to direct hydroxide catalyzed hydrolysis (to 3). Concomitantly, neutral amide participation is observed so that cyclization of 1 (Ar = p-NO₂, m-NO₂, m-Cl, p-ClC₆H₄) occurs even in acidic solution; the Hammett ? values for neutral and base catalysed cyclizations are compared. Hydrolysis of methyl-N-acetylanthranilate 6 to 3 occurs slowly in base, possibly without the formation of the intermediate 4.     

Sephadex-bound histamine in the catalysis of ester hydrolysis

Ester hydrolysis by Sephadex-bound catalysts was studied in a flow-through system. Three different immobilized preparations were synthesized and used: histamine-, coimmobilized histamine-octylamine-, and octylamine-Sephadex; octylamine-Sephadex was used as a reference. Immobilization was carried out using water-soluble carbodiimide, which gave amide linkages between carboxymethyl Sephadex and the groups attached. It was found that the coimmobilized histamine-octylamine preparation was three times more efficient than immobilized histamine alone in the hydrolysis of the esterp-nitrophenylcaproate, whereas hardly any difference was found in the hydrolysis of the less hydrophobic substratep-nitrophenylacetate. We attribute this enhancement of the hydrolysis ofp-nitrophenylcaproate to local enrichment of the substrate on the histamine-octylamine matrix caused by the presence of hydrophobic octyl groups.     

Determination of the hydrolysis rate constants and activation energy of aesculin with capillary electrophoresis end-column amperometric detection

Indirect chemiluminescence (ICL) detection for capillary electrophoresis (CE) of monoamines and catechol using luminol-K3 [Fe(CN)6] system was described. A strong and stable background chemiluminescence (CL) signal can be generated by luminol-K3 [Fe(CN)6] reaction. Based on the principle of that some phenolic compounds may be oxidized in the presence of K3 [Fe(CN)6], quenching effect of catecholamines for luminol-K3[Fe(CN)6] CL reaction results in a quantifiable decrease in the background signal. The conditions for CE separation and the CL detection for four standard catecholamines were systematically investigated using a homemade CE-ICL system. Under the optimum conditions, the detection limits of dopamine (DA), epinephrine (EP), norepinephrine (NE) and catechol (CA) were determined to be 0.18 mciroM 0.39 microM 0.48 microM and 0.09 microM, respectively. It also has been successfully applied to analyze seven pharmaceutical samples and seven human urine samples.     

Activation enthalpies and entropies for the microscopic rate constants of acetate-catalyzed isomerization of 5-androstene-3,17-dione

Both acetic acid and acetate catalyze the isomerization of 5-androstene-3,17-dione (1) to its conjugated isomer, 4-androstene-3,17-dione (3), through a dienol(ate) intermediate. The temperature dependence of the overall isomerization rate constants and of the microscopic rate constants for this isomerization was determined, and the Arrhenius plots give the activation enthalpy and entropy for each step. The source of the activation energy for the overall isomerization and for each of the individual steps is predominantly enthalpic, with a moderate to low entropic penalty. Additionally, the entropy and enthalpy for the keto-enol equilibrium of 1 and dienol were determined; this equilibrium is entirely controlled by enthalpy with no entropic contribution. The relevance of these results to the mechanism of the isomerization of 1 catalyzed by the enzyme 3-oxo-Delta(5)-steroid isomerase is discussed.     

The role of metal ions in phosphate ester hydrolysis

Many phosphatases make use of metal ions to aid catalysis of phosphate ester hydrolysis. Here, we investigate the impact of metal ions on the potential energy surface (PES), and hence the preferred reaction mechanism, for a simple model for hydrolysis of phosphate ester monoanions. We show that, while both associative (A(N) + D(N)) and dissociative (D(N) + A(N)) mechanisms are represented on the potential energy surfaces both in the presence and absence of metal ions, the D(N) + A(N) process is favoured when there are no metal ions present and the A(N) + D(N) process is favoured in the presence of two metal ions. A concerted (A(N)D(N)) process is also available in the presence of two metal ions, but proceeds via a high-energy transition state. In the presence of only a single metal ion the A(N)D(N) process is the most favoured, but still proceeds via a high-energy transition state. Thus, we conclude that metallo-enzyme phosphatases are likely to utilise an associative process, while those that function without metal ions may well follow a dissociative process.     

On reaction rate constants and rate kernels

A simple model for a reversible isomerization reaction A ? B is used to show how rate constants and their time-dependent generalizations can be related to microscopic reactive steps and nonreactive internal dynamics (e.g., vibrational relaxation).     

Termination rate constants in radical polymerization

A rate constant is generally derived by using Fick's equation corresponding to the spherical interdiffusion of particles. By using this rate constant, chain and primary radical termination rate constants can be approximated to rate constants for the bimolecular reactions between two radical chain ends, and primary radical and radical chain end, respectively. The former is given by k_s = 8πN_LD_sL_s exp { ? L_s/R_s} × 10^?3 1./mole-sec. The latter is given by k_si = 4πN_L(D_s + D_i)L_si exp { ? L_si/R_si} × 10^?3 1./mole-sec. Here, N_L is Avogadro's number; D_s and D_i are the diffusion constants of radical chain end and primary radical, respectively; L_s and L_si are, respectively, the distances between two radical chain ends and between a primary radical and a radical chain end at a thermal energy equal to the coulombic energy of interaction of the net charges; and R_s and R_si are, respectively, the average distances between two radical chain ends and primary radical on a collision.     

Enantioselective ester hydrolysis catalyzed by imprinted polymers

Highly cross-linked network polymers prepared by molecular imprinting catalyzed enantioselectively the hydrolysis of N-tert-butoxycarbonyl phenylalanine-p-nitrophenyl ester (BOCPheONP). The templates were designed to allow incorporation of the key catalytic elements, found in the proteolytic enzyme chymotrypsin, into the polymer active sites. Three model systems were evaluated. These were constructed from a chiral phosphonate analogue of phenylalanine (series A, C) or L-phenylalanine (series B) attached by a labile ester linkage to an imidazole-containing vinyl monomer. Free radical copolymerization of the template with methacrylic acid (MAA) and ethylene glycol dimethacrylate (EDMA) gave a highly cross-linked network polymer. The templates could be liberated from the polymers by hydrolysis, giving catalytically active sites envisaged to contain an enantioselective binding site, a site complementary to a transition state like structure (series A, C), and a hydroxyl, imidazole, and carboxylic acid group at hydrogen bond distance. As predicted, the enantiomer of BOCPheONP complementary to the configuration of the template was preferentially hydrolyzed with D-selectivity for the series A polymers (kD/kL = 1.9) and L-selectivity for the series B polymers (kL/kD = 1.2). The maximum rate enhancement, when compared with a control polymer, prepared using a benzoyl-substituted imidazole monomer as template, was 2.5, and comparing with the imidazole monomer in solution, a maximum rate enhancement of 10 was observed. The catalytic activity was higher for polymers subjected to the nucleophilic treatment. This was explained by a higher site density and flexibility of the polymer matrix caused by this treatment. In a comparison of template rebinding to polymers imprinted with a template containing either a carboxylate (planar ground state structure) or a phosphonate (tetrahedral transition state like structure) functionality, it was observed that imprinted polymers are able to discriminate between a transition state like and a ground state structure for transesterification. However the influence of transition state stabilization on the observed rate enhancements remains obscure. Only at acidic pH's was catalysis observed, whereas at basic pH's the polymers inhibit the reaction. At a later stage, the catalytic activity of the polymers for nonactivated D- and L-phenylalanine ethyl esters was investigated. A rate enhancement of up to 3 was observed when compared to the blank. Most important, however, the polymers imprinted with a D template preferentially hydrolyzed the D-ethyl ester and exhibited saturation kinetics.     

Mathematical formulas for ester hydrolysis and formation

Mathematical formulas are developed to describe the progress of ester hydrolysis reactions and the reverse reactions of ester formation, in aqueous solution. Included is a formula for the time to achieve a given degree of reaction. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 277–280, 2001     

The relative importance of delocalization terms in proton spin-spin coupling constants

An expression for the atom-atom poiarizability between the1s orbitals of geminal or vicinal protons has been derived by perturbation theory using thePople-Santry Theory of electron systems. The coupling constants calculated on this basis agree well with these obtained from full molecular orbital calculations. Expressions have been obtained for the variation of vicinal coupling constants with dihedral angle in ethane and the HCC bond angle and C-C bond length in ethylene, and these agree well with corresponding expressions obtained using the VB method.

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Zusammenfassung Es wurde ein Ausdruck für die Atom-Atom-Polarisierbarkeit zwischen den1s Orbitalen geminaler bzw. vicinaler Protonen abgeleitet mittels Störungsrechnung unter Benutzung derPople-Santry-Theorie für-Elektronensysteme. Die auf dieser Basis berechneten Koppelungskonstanten stimmen gut mit denen aus einer vollständigen MO Rechnung überein. Es wurden Ausdrücke erhalten für die Änderung der vicinalen Koppelungskonstanten mit dem Diederwinkel in Äthan sowie dem HOC Bindungswinkel und der C-C Bindungsiänge in Äthylen, die gut mit den entsprechenden Ausdrücken aus der VB Methode übereinstimmen.

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Résumé A l'aide de la théorie dePople etSantry sur les systèmes d'électrons, nous dérivons de la théorie des perturbations une expression pour la polarisabiiité atome-atome entre les orbitales1s des protons géminaux ou vicinaux. Les constantes de couplage ici calculées s'accordent bien à celles obtenues des calculs OM complets. Les expressions obtenues pour la variation du couplage vicinal avec l'angle dihédrique dans l'éthane, et l'angle HCC et la distance C-C dans l'éthylène, s'accordent bien aux formules correspondantes de la méthode de la mésomérie.

     

The thermodynamics of phosphate versus phosphorothioate ester hydrolysis

Phosphorothioate esters are phosphate esters in which one of the nonbridging oxygen atoms has been replaced by sulfur. In the comparative hydrolysis reactions of phosphorothioate and phosphate esters, the sulfur substitution accelerates the rates of the monoesters while slowing the rates of diesters and of triesters. Previously measured enthalpies and entropies of activation for the hydrolysis reactions of the monoesters, p-nitrophenyl phosphate and p-nitrophenyl phosphorothioate, were compared to the activation parameters measured herein for the diesters, ethyl p-nitrophenyl phosphate and ethyl p-nitrophenyl phosphorothioate, and the triesters, diethyl p-nitrophenyl phosphate and diethyl p-nitrophenyl phosphorothioate. A consistent trend of a greater DeltaH++ for the phosphorothioate analogue was found in all three classes of ester. In the monoester case, a more positive DeltaS++ arising from a mechanistic difference (D(N) + A(N) for the phosphorothioate versus A(N)D(N) for the phosphate) compensates, resulting in a lower DeltaG++ for the phosphorothioate monoester. Spectroscopic investigations indicate there is no significant difference in bond order to the leaving group in phosphates, as compared to their phosphorothioate analogues, ruling this out as a contribution to the consistently higher enthalpies of activation.     

Intramolecular general base catalyzed ester hydrolysis. The hydrolysis of 2-aminobenzoate esters

Rate constants have been obtained for the hydrolysis of the trifluoroethyl, phenyl, and p-nitrophenyl esters of 2-aminobenzoic acid at 50 degrees C in H(2)O. The pseudo-first-order rate constants, k(obsd), are pH independent from pH 8 to pH 4 (the pK(a) of the amine group conjugate acid). The 2-aminobenzoate esters hydrolyze with similar rate constants in the pH-independent reactions, and these water reactions are approximately 2-fold slower in D(2)O than in H(2)O. The most likely mechanism involves intramolecular general base catalysis by the neighboring amine group. The rate enhancements in the pH-independent reaction in comparison with the pH-independent hydrolysis of the corresponding para substituted esters or the benzoate esters are 50-100-fold. In comparison with the hydroxide ion catalyzed reaction, the enhancement in k(obsd) at pH 4 with the phenyl ester is 10(5)-fold. Intramolecular general base catalyzed reactions are assessed in respect to their relative advantages and disadvantages in enzyme catalysis. A general base catalyzed reaction can be more rapid at low pH than a nucleophilic reaction that has a marked dependence on pH and the leaving group.